Uniqueness of \(L\) function with special class of meromorphic function under restricted sharing of sets. (English) Zbl 1483.11190
Summary: The purpose of the paper is to rectify a series of errors occurred in [A. Banerjee and A. Kundu, Lith. Math. J. 61, No. 2, 161–179 (2021; Zbl 1469.11341); P. Sahoo and A. Sarkar, An. Științ. Univ. Al. I. Cuza Iași, Ser. Nouă, Mat. 66, No. 1, 81–92 (2020; Zbl 1474.11153); Q.-Q. Yuan et al., Lith. Math. J. 58, No. 2, 249–262 (2018; Zbl 1439.11231)] for a particular situation. To get a fruitful solution and to overcome the issue, we introduce a new form of set sharing namely restricted set sharing, which is stronger than the usual one. We manipulate the newly introduced notion in this specific section of literature to resolve all the complications. Not only that we have subtly used the same sharing form to a well known unique range set [G. Frank and M. Reinders, Complex Variables, Theory Appl. 37, No. 1–4, 185–193 (1998; Zbl 1054.30519)] to settle a long time unsolved problem.
MSC:
| 11M36 | Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) |
| 30D35 | Value distribution of meromorphic functions of one complex variable, Nevanlinna theory |
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